CAJ | 학술논문

逻辑矛盾仅是“量词-质词-真值词”皆矛盾的非等值关系命题，辩证矛盾仅是“主词-谓词-命题词”皆矛盾的等值关系命题。在以事实验证了一元与二元真值函数的断定一致性和能指完全性基础上，说明哥德尔定理对包含扩充自然数后的代数理论并不适用。为了实现形式系统可兼容的一致性和完全性，必须引进所指有辩证矛盾和断言无逻辑矛盾之“指断合一”的哲学对象论。由此用基于负号而推广的辩证否定算子，才能彻底根治一阶逻辑形式系统的不完全性。
라집모순부시“량사-질사-진치사”개모순적비등치관계명제，변증모순부시“주사-위사-명제사”개모순적등치관계명제。재이사실험증료일원여이원진치함수적단정일치성화능지완전성기출상，설명가덕이정리대포함확충자연수후적대수이론병불괄용。위료실현형식계통가겸용적일치성화완전성，필수인진소지유변증모순화단언무라집모순지“지단합일”적철학대상론。유차용기우부호이추엄적변증부정산자，재능철저근치일계라집형식계통적불완전성。
Logic contradiction is only non equivalent relation proposition of all contradictive quantifier, quality word, true value word ; dialectical contradiction is only equivalent relation proposition of all contradictive subject term, object term and proposition term. Based on the fact to verify the posit consistence and integrity to show that Gtidel＇s law is not applicable to algebraic theory including expended natural number. In order to realize consistence and integrity compatible of formal system, philosophy object theory included dialectical contradiction and predictive non-logic contradiction must be introduced. So by using dialectical negative operator extended on negative sign can total solve the nonintegrity of first order logic formalization system.